Why would any centralized company/organization wants to use blockchain? they are in control of everything and they have all the records.
It's not like banks trying to double spend their own money, since people can't access their system there is no need to implement such technology.
Becasue they're connected to each other, and they're using an old and slow system at the moment to exchange data between their systems. World is changing, now, when you can send an email in some minutes to the farest country, why your money would still remain slow? Today, if you want to transfer money from a bank to another bank in a different county, you have to wait 2-3 days. If banks have a blockchain based clearing system, they will clear transactions in an hour, and not in 2-3 days time. This is the goal, this is why they're trying to find a solution, but as long as they are only developing the technology, it's quite a slow process.